For linear media of which the index of refraction changes slowly in the propagation direction, the WKB method is presented as a transformation that enables a simple approach towards higher order approximations. For homogeneous non-linear media the SVEA method considers small amplitude approximations that change slowly in spatial directions. For third order non-linear media with a slowly varying index of refraction, the combination of WKB and SVEA lead to a two-parameter problem; relating the amplitude in a specific way to the measure of the slow medium changes, transformations are given that lead to a NLS equation with slowly varying coefficients and even to NLS with constant coefficients.